If the circles x^2+y^2+2ax+c^2=0 and x^2+y^2+2by+c^2=0 touch each other,prove that 1/a^2+1/b^2=1/c^2?
#1/a^2+1/b^2=1/c^2#
1 Answer
Feb 20, 2018
See below
Explanation:
If the two circles touch each other, they must have one and only one point in common.
This point must satisfy both
and
so that
Substituting
Since the circles touch each other, this quadratic must have equal roots, so